Acronym | tix (alt.: pentum) |
Name |
truncated hexateron, pen-based tutism |
Field of sections |
© |
Circumradius | sqrt(7)/2 = 1.322876 |
Inradius wrt. pen | sqrt(27/20) = 1.161895 |
Inradius wrt. tip | sqrt(3/20) = 0.387298 |
Vertex figure |
© © |
Lace city in approx. ASCII-art |
o3o3o x3o3o -- x3o3o3o (pen) o3o3o u3o3o -- u3o3o3o (u-pen) x3o3o u3o3o x3x3o -- x3x3o3o (tip) |
Volume | 79 sqrt(3)/160 = 0.855200 |
Surface | 77 sqrt(5)/16 = 10.761077 |
Dihedral angles
(at margins) | |
Face vector | 30, 75, 80, 45, 12 |
Confer |
|
External links |
Incidence matrix according to Dynkin symbol
x3x3o3o3o . . . . . | 30 | 1 4 | 4 6 | 6 4 | 4 1 ----------+----+-------+-------+-------+---- x . . . . | 2 | 15 * ♦ 4 0 | 6 0 | 4 0 . x . . . | 2 | * 60 | 1 3 | 3 3 | 3 1 ----------+----+-------+-------+-------+---- x3x . . . | 6 | 3 3 | 20 * | 3 0 | 6 0 . x3o . . | 3 | 0 3 | * 60 | 1 2 | 2 1 ----------+----+-------+-------+-------+---- x3x3o . . ♦ 12 | 6 12 | 4 4 | 15 * | 2 0 . x3o3o . ♦ 4 | 0 6 | 0 4 | * 30 | 1 1 ----------+----+-------+-------+-------+---- x3x3o3o . ♦ 20 | 10 30 | 10 20 | 5 5 | 6 * . x3o3o3o ♦ 5 | 0 10 | 0 10 | 0 5 | * 6
x3x3o3o3/2o . . . . . | 30 | 1 4 | 4 6 | 6 4 | 4 1 ------------+----+-------+-------+-------+---- x . . . . | 2 | 15 * ♦ 4 0 | 6 0 | 4 0 . x . . . | 2 | * 60 | 1 3 | 3 3 | 3 1 ------------+----+-------+-------+-------+---- x3x . . . | 6 | 3 3 | 20 * | 3 0 | 6 0 . x3o . . | 3 | 0 3 | * 60 | 1 2 | 2 1 ------------+----+-------+-------+-------+---- x3x3o . . ♦ 12 | 6 12 | 4 4 | 15 * | 2 0 . x3o3o . ♦ 4 | 0 6 | 0 4 | * 30 | 1 1 ------------+----+-------+-------+-------+---- x3x3o3o . ♦ 20 | 10 30 | 10 20 | 5 5 | 6 * . x3o3o3/2o ♦ 5 | 0 10 | 0 10 | 0 5 | * 6
xux3oox3ooo3ooo&#xt → both heights = sqrt(3/5) = 0.774597 (pen || pseudo u-pen || tip) o..3o..3o..3o.. | 5 * * | 4 1 0 0 0 | 6 4 0 0 0 | 4 6 0 0 0 | 1 4 0 0 .o.3.o.3.o.3.o. | * 5 * | 0 1 4 0 0 | 0 4 6 0 0 | 0 6 4 0 0 | 0 4 1 0 ..o3..o3..o3..o | * * 20 | 0 0 1 1 3 | 0 1 3 3 3 | 0 3 3 3 1 | 0 3 1 1 --------------------+--------+---------------+----------------+-------------+-------- x.. ... ... ... | 2 0 0 | 10 * * * * | 3 1 0 0 0 | 3 3 0 0 0 | 1 3 0 0 oo.3oo.3oo.3oo.&#x | 1 1 0 | * 5 * * * ♦ 0 4 0 0 0 | 0 6 0 0 0 | 0 4 0 0 .oo3.oo3.oo3.oo&#x | 0 1 1 | * * 20 * * | 0 1 3 0 0 | 0 3 3 0 0 | 0 3 1 0 ..x ... ... ... | 0 0 2 | * * * 10 * ♦ 0 1 0 3 0 | 0 3 0 3 0 | 0 3 0 1 ... ..x ... ... | 0 0 2 | * * * * 30 | 0 0 1 1 2 | 0 1 2 2 1 | 0 2 1 1 --------------------+--------+---------------+----------------+-------------+-------- x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 | 10 * * * * | 2 1 0 0 0 | 1 2 0 0 xux ... ... ...&#xt | 2 2 2 | 1 2 2 1 0 | * 10 * * * | 0 3 0 0 0 | 0 3 0 0 ... .ox ... ...&#x | 0 1 2 | 0 0 2 0 1 | * * 30 * * | 0 1 2 0 0 | 0 2 1 0 ..x3..x ... ... | 0 0 6 | 0 0 0 3 3 | * * * 10 * | 0 1 0 2 0 | 0 2 0 1 ... ..x3..o ... | 0 0 3 | 0 0 0 0 3 | * * * * 20 | 0 0 1 1 1 | 0 1 1 1 --------------------+--------+---------------+----------------+-------------+-------- x..3o..3o.. ... ♦ 4 0 0 | 6 0 0 0 0 | 4 0 0 0 0 | 5 * * * * | 1 1 0 0 xux3oox ... ...&#xt ♦ 3 3 6 | 3 3 6 3 3 | 1 3 3 1 0 | * 10 * * * | 0 2 0 0 ... .ox3.oo ...&#x ♦ 0 1 3 | 0 0 3 0 3 | 0 0 3 0 1 | * * 20 * * | 0 1 1 0 ..x3..x3..o ... ♦ 0 0 12 | 0 0 0 6 12 | 0 0 0 4 4 | * * * 5 * | 0 1 0 1 ... ..x3..o3..o ♦ 0 0 4 | 0 0 0 0 6 | 0 0 0 0 4 | * * * * 5 | 0 0 1 1 --------------------+--------+---------------+----------------+-------------+-------- x..3o..3o..3o.. ♦ 5 0 0 | 10 0 0 0 0 | 10 0 0 0 0 | 5 0 0 0 0 | 1 * * * xux3oox3ooo ...&#xt ♦ 4 4 12 | 6 4 12 6 12 | 4 6 12 4 4 | 1 4 4 1 0 | * 5 * * ... .ox3.oo3.oo&#x ♦ 0 1 4 | 0 0 4 0 6 | 0 0 6 0 4 | 0 0 4 0 1 | * * 5 * ..x3..x3..o3..o ♦ 0 0 20 | 0 0 0 10 30 | 0 0 0 10 20 | 0 0 0 5 5 | * * * 1
xuxo oxux3ooox3oooo&#xt → all heights = sqrt(3/8) = 0.612372 (line || pseudo (x,u)-tepe || pseudo (u,x)-tepe || tut) o... o...3o...3o... | 2 * * * | 1 4 0 0 0 0 0 0 | 6 4 0 0 0 0 0 0 | 4 6 0 0 0 0 0 | 1 4 0 0 .o.. .o..3.o..3.o.. | * 8 * * | 0 1 3 1 0 0 0 0 | 3 1 3 3 0 0 0 0 | 3 3 1 3 0 0 0 | 1 3 1 0 ..o. ..o.3..o.3..o. | * * 8 * | 0 0 0 1 1 3 0 0 | 0 1 0 3 3 3 0 0 | 0 3 0 3 3 1 0 | 0 3 1 1 ...o ...o3...o3...o | * * * 12 | 0 0 0 0 0 2 1 2 | 0 0 0 2 1 4 2 1 | 0 1 0 4 2 2 1 | 0 2 2 1 ------------------------+----------+--------------------+---------------------+----------------+-------- x... .... .... .... | 2 0 0 0 | 1 * * * * * * * ♦ 0 4 0 0 0 0 0 0 | 0 6 0 0 0 0 0 | 0 4 0 0 oo.. oo..3oo..3oo..&#x | 1 1 0 0 | * 8 * * * * * * | 3 1 0 0 0 0 0 0 | 3 3 0 0 0 0 0 | 1 3 0 0 .... .x.. .... .... | 0 2 0 0 | * * 12 * * * * * | 1 0 2 1 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0 .oo. .oo.3.oo.3.oo.&#x | 0 1 1 0 | * * * 8 * * * * ♦ 0 1 0 3 0 0 0 0 | 0 3 0 3 0 0 0 | 0 3 1 0 ..x. .... .... .... | 0 0 2 0 | * * * * 4 * * * | 0 1 0 0 3 0 0 0 | 0 3 0 0 3 0 0 | 0 3 0 1 ..oo ..oo3..oo3..oo&#x | 0 0 1 1 | * * * * * 24 * * | 0 0 0 1 1 2 0 0 | 0 1 0 2 2 1 0 | 0 2 1 1 .... ...x .... .... | 0 0 0 2 | * * * * * * 6 * ♦ 0 0 0 2 0 0 2 0 | 0 1 0 4 0 0 1 | 0 2 2 0 .... .... ...x .... | 0 0 0 2 | * * * * * * * 12 | 0 0 0 0 0 2 1 1 | 0 0 0 2 1 2 1 | 0 1 2 1 ------------------------+----------+--------------------+---------------------+----------------+-------- .... ox.. .... ....&#x | 1 2 0 0 | 0 2 1 0 0 0 0 0 | 12 * * * * * * * | 2 1 0 0 0 0 0 | 1 2 0 0 xux. .... .... ....&#xt | 2 2 2 0 | 1 2 0 2 1 0 0 0 | * 4 * * * * * * | 0 3 0 0 0 0 0 | 0 3 0 0 .... .x..3.o.. .... | 0 3 0 0 | 0 0 3 0 0 0 0 0 | * * 8 * * * * * | 1 0 1 1 0 0 0 | 1 1 1 0 .... .xux .... ....&#xt | 0 2 2 2 | 0 0 1 2 0 2 1 0 | * * * 12 * * * * | 0 1 0 2 0 0 0 | 0 2 1 0 ..xo .... .... ....&#x | 0 0 2 1 | 0 0 0 0 1 2 0 0 | * * * * 12 * * * | 0 1 0 0 2 0 0 | 0 2 0 1 .... .... ..ox ....&#x | 0 0 1 2 | 0 0 0 0 0 2 0 1 | * * * * * 24 * * | 0 0 0 1 1 1 0 | 0 1 1 1 .... ...x3...x .... | 0 0 0 6 | 0 0 0 0 0 0 3 3 | * * * * * * 4 * | 0 0 0 2 0 0 1 | 0 1 2 0 .... .... ...x3...o | 0 0 0 3 | 0 0 0 0 0 0 0 3 | * * * * * * * 4 | 0 0 0 0 0 2 1 | 0 0 2 1 ------------------------+----------+--------------------+---------------------+----------------+-------- .... ox..3oo.. ....&#x ♦ 1 3 0 0 | 0 3 3 0 0 0 0 0 | 3 0 1 0 0 0 0 0 | 8 * * * * * * | 1 1 0 0 xuxo oxux .... ....&#xt ♦ 2 4 4 2 | 1 4 2 4 2 4 1 0 | 2 2 0 2 2 0 0 0 | * 6 * * * * * | 0 2 0 0 .... .x..3.o..3.o.. ♦ 0 4 0 0 | 0 0 6 0 0 0 0 0 | 0 0 4 0 0 0 0 0 | * * 2 * * * * | 1 0 1 0 .... .xux3.oox ....&#xt ♦ 0 3 3 6 | 0 0 3 3 0 6 3 3 | 0 0 1 3 0 3 1 0 | * * * 8 * * * | 0 1 1 0 ..xo .... ..ox ....&#x ♦ 0 0 2 2 | 0 0 0 0 1 4 0 1 | 0 0 0 0 2 2 0 0 | * * * * 12 * * | 0 1 0 1 .... .... ..ox3..oo&#x ♦ 0 0 1 3 | 0 0 0 0 0 3 0 3 | 0 0 0 0 0 3 0 1 | * * * * * 8 * | 0 0 1 1 .... ...x3...x3...o ♦ 0 0 0 12 | 0 0 0 0 0 0 6 12 | 0 0 0 0 0 0 4 4 | * * * * * * 1 | 0 0 2 0 ------------------------+----------+--------------------+---------------------+----------------+-------- .... ox..3oo..3oo..&#x ♦ 1 4 0 0 | 0 4 6 0 0 0 0 0 | 6 0 4 0 0 0 0 0 | 4 0 1 0 0 0 0 | 2 * * * xuxo oxux3ooox ....&#xt ♦ 2 6 6 6 | 1 6 6 6 3 12 3 3 | 6 3 2 6 6 6 1 0 | 2 3 0 2 3 0 0 | * 4 * * .... .xux3.oox3.ooo&#xt ♦ 0 4 4 12 | 0 0 6 4 0 12 6 12 | 0 0 4 6 0 12 4 4 | 0 0 1 4 0 4 1 | * * 2 * ..xo .... ..ox3..oo&#x ♦ 0 0 2 3 | 0 0 0 0 1 6 0 3 | 0 0 0 0 3 6 0 1 | 0 0 0 0 3 2 0 | * * * 4
xuxo3xooo oxux3ooox&#xt → all heights = 1/sqrt(3) = 0.577350 ({6} || pseudo (u,x)-triddip || pseudo (x,u)-triddip || perp {6}) o...3o... o...3o... | 6 * * * | 1 1 3 0 0 0 0 0 0 | 1 3 3 3 0 0 0 0 0 0 | 3 1 3 3 0 0 0 | 1 3 1 0 .o..3.o.. .o..3.o.. | * 9 * * | 0 0 2 2 1 0 0 0 0 | 0 1 4 2 1 2 0 0 0 0 | 2 2 1 4 1 0 0 | 1 2 2 0 ..o.3..o. ..o.3..o. | * * 9 * | 0 0 0 0 1 2 2 0 0 | 0 0 0 2 0 2 1 4 1 0 | 0 0 1 4 1 2 2 | 0 2 2 1 ...o3...o ...o3...o | * * * 6 | 0 0 0 0 0 0 3 1 1 | 0 0 0 0 0 3 0 3 3 1 | 0 0 0 3 3 1 3 | 0 1 3 1 ------------------------+---------+---------------------+-----------------------+---------------+-------- x... .... .... .... | 2 0 0 0 | 3 * * * * * * * * ♦ 1 0 0 3 0 0 0 0 0 0 | 0 0 3 3 0 0 0 | 0 3 1 0 .... x... .... .... | 2 0 0 0 | * 3 * * * * * * * | 1 3 0 0 0 0 0 0 0 0 | 3 0 3 0 0 0 0 | 1 3 0 0 oo..3oo.. oo..3oo..&#x | 1 1 0 0 | * * 18 * * * * * * | 0 1 2 1 0 0 0 0 0 0 | 2 1 1 2 0 0 0 | 1 2 1 0 .... .... .x.. .... | 0 2 0 0 | * * * 9 * * * * * | 0 0 2 0 1 1 0 0 0 0 | 1 2 0 2 1 0 0 | 1 1 2 0 .oo.3.oo. .oo.3.oo.&#x | 0 1 1 0 | * * * * 9 * * * * ♦ 0 0 0 2 0 2 0 0 0 0 | 0 0 1 4 1 0 0 | 0 2 2 0 ..x. .... .... .... | 0 0 2 0 | * * * * * 9 * * * | 0 0 0 1 0 0 1 2 0 0 | 0 0 1 2 0 2 1 | 0 2 1 1 ..oo3..oo ..oo3..oo&#x | 0 0 1 1 | * * * * * * 18 * * | 0 0 0 0 0 1 0 2 1 0 | 0 0 0 2 1 1 2 | 0 1 2 1 .... .... ...x .... | 0 0 0 2 | * * * * * * * 3 * ♦ 0 0 0 0 0 3 0 0 0 1 | 0 0 0 3 3 0 0 | 0 1 3 0 .... .... .... ...x | 0 0 0 2 | * * * * * * * * 3 | 0 0 0 0 0 0 0 0 3 1 | 0 0 0 0 3 0 3 | 0 0 3 1 ------------------------+---------+---------------------+-----------------------+---------------+-------- x...3x... .... .... | 6 0 0 0 | 3 3 0 0 0 0 0 0 0 | 1 * * * * * * * * * | 0 0 3 0 0 0 0 | 0 3 0 0 .... xo.. .... ....&#x | 2 1 0 0 | 0 1 2 0 0 0 0 0 0 | * 9 * * * * * * * * | 2 0 1 0 0 0 0 | 1 2 0 0 .... .... ox.. ....&#x | 1 2 0 0 | 0 0 2 1 0 0 0 0 0 | * * 18 * * * * * * * | 1 1 0 1 0 0 0 | 1 1 1 0 xux. .... .... ....&#xt | 2 2 2 0 | 1 0 2 0 2 1 0 0 0 | * * * 9 * * * * * * | 0 0 1 2 0 0 0 | 0 2 1 0 .... .... .x..3.o.. | 0 3 0 0 | 0 0 0 3 0 0 0 0 0 | * * * * 3 * * * * * | 0 2 0 0 1 0 0 | 1 0 2 0 .... .... .xux ....&#xt | 0 2 2 2 | 0 0 0 1 2 0 2 1 0 | * * * * * 9 * * * * | 0 0 0 2 1 0 0 | 0 1 2 0 ..x.3..o. .... .... | 0 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * 3 * * * | 0 0 1 0 0 2 0 | 0 2 0 1 ..xo .... .... ....&#x | 0 0 2 1 | 0 0 0 0 0 1 2 0 0 | * * * * * * * 18 * * | 0 0 0 1 0 1 1 | 0 1 1 1 .... .... .... ..ox&#x | 0 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * * * * 9 * | 0 0 0 0 1 0 2 | 0 0 2 1 .... .... ...x3...x | 0 0 0 6 | 0 0 0 0 0 0 0 3 3 | * * * * * * * * * 1 | 0 0 0 0 3 0 0 | 0 0 3 0 ------------------------+---------+---------------------+-----------------------+---------------+-------- .... xo.. ox.. ....&#x ♦ 2 2 0 0 | 0 1 4 1 0 0 0 0 0 | 0 2 2 0 0 0 0 0 0 0 | 9 * * * * * * | 1 1 0 0 .... .... ox..3oo..&#x ♦ 1 3 0 0 | 0 0 3 3 0 0 0 0 0 | 0 0 3 0 1 0 0 0 0 0 | * 6 * * * * * | 1 0 1 0 xux.3xoo. .... ....&#xt ♦ 6 3 3 0 | 3 3 6 0 3 3 0 0 0 | 1 3 0 3 0 0 1 0 0 0 | * * 3 * * * * | 0 2 0 0 xuxo .... oxux ....&#xt ♦ 2 4 4 2 | 1 0 4 2 4 2 4 1 0 | 0 0 2 2 0 2 0 2 0 0 | * * * 9 * * * | 0 1 1 0 .... .... .xux3.oox&#xt ♦ 0 3 3 6 | 0 0 0 3 3 0 6 3 3 | 0 0 0 0 1 3 0 0 3 1 | * * * * 3 * * | 0 0 2 0 ..xo3..oo .... ....&#x ♦ 0 0 3 1 | 0 0 0 0 0 3 3 0 0 | 0 0 0 0 0 0 1 3 0 0 | * * * * * 6 * | 0 1 0 1 ..xo .... .... ..ox&#x ♦ 0 0 2 2 | 0 0 0 0 0 1 4 0 1 | 0 0 0 0 0 0 0 2 2 0 | * * * * * * 9 | 0 0 1 1 ------------------------+---------+---------------------+-----------------------+---------------+-------- .... xo.. ox..3oo..&#x ♦ 2 3 0 0 | 0 1 6 3 0 0 0 0 0 | 0 3 6 0 1 0 0 0 0 0 | 3 2 0 0 0 0 0 | 3 * * * xuxo3xooo oxux ....&#xt ♦ 6 6 6 2 | 3 3 12 3 6 6 6 1 0 | 1 6 6 6 0 3 2 6 0 0 | 3 0 2 3 0 2 0 | * 3 * * xuxo .... oxux3ooox&#xt ♦ 2 6 6 6 | 1 0 6 6 6 3 12 3 3 | 0 0 6 3 2 6 0 6 6 1 | 0 2 0 3 2 0 3 | * * 3 * ..xo3..oo .... ..ox&#x ♦ 0 0 3 2 | 0 0 0 0 0 3 6 0 1 | 0 0 0 0 0 0 1 6 3 0 | 0 0 0 0 0 2 3 | * * * 3
or o...3o... o...3o... & | 12 * | 1 1 3 0 0 | 1 3 3 3 0 | 3 1 3 3 | 1 4 .o..3.o.. .o..3.o.. & | * 18 | 0 0 2 2 1 | 0 1 4 4 1 | 2 2 2 4 | 1 4 ---------------------------+-------+-------------+--------------+-----------+---- x... .... .... .... & | 2 0 | 6 * * * * ♦ 1 0 0 3 0 | 0 0 3 3 | 0 4 .... x... .... .... & | 2 0 | * 6 * * * | 1 3 0 0 0 | 3 0 3 0 | 1 3 oo..3oo.. oo..3oo..&#x & | 1 1 | * * 36 * * | 0 1 2 1 0 | 2 1 1 2 | 1 3 .... .... .x.. .... & | 0 2 | * * * 18 * | 0 0 2 1 1 | 1 2 1 2 | 1 3 .oo.3.oo. .oo.3.oo.&#x | 0 2 | * * * * 9 ♦ 0 0 0 4 0 | 0 0 2 4 | 0 4 ---------------------------+-------+-------------+--------------+-----------+---- x...3x... .... .... & | 6 0 | 3 3 0 0 0 | 2 * * * * | 0 0 3 0 | 0 3 .... xo.. .... ....&#x & | 2 1 | 0 1 2 0 0 | * 18 * * * | 2 0 1 0 | 1 2 .... .... ox.. ....&#x & | 1 2 | 0 0 2 1 0 | * * 36 * * | 1 1 0 1 | 1 2 xux. .... .... ....&#xt & | 2 4 | 1 0 2 1 2 | * * * 18 * | 0 0 1 2 | 0 3 .... .... .x..3.o.. & | 0 3 | 0 0 0 3 0 | * * * * 6 | 0 2 1 0 | 1 2 ---------------------------+-------+-------------+--------------+-----------+---- .... xo.. ox.. ....&#x & ♦ 2 2 | 0 1 4 1 0 | 0 2 2 0 0 | 18 * * * | 1 1 .... .... ox..3oo..&#x & ♦ 1 3 | 0 0 3 3 0 | 0 0 3 0 1 | * 12 * * | 1 1 xux.3xoo. .... ....&#xt & ♦ 6 6 | 3 3 6 3 3 | 1 3 0 3 1 | * * 6 * | 0 2 xuxo .... oxux ....&#xt ♦ 4 8 | 2 0 8 4 4 | 0 0 4 4 0 | * * * 9 | 0 2 ---------------------------+-------+-------------+--------------+-----------+---- .... xo.. ox..3oo..&#x & ♦ 2 3 | 0 1 6 3 0 | 0 3 6 0 1 | 3 2 0 0 | 6 * xuxo3xooo oxux ....&#xt & ♦ 8 12 | 4 3 18 9 6 | 1 6 12 9 2 | 3 2 2 3 | * 6
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